(389f) Distributed Model Predictive Control of Nonlinear Systems Subject to Asynchronous and Delayed Measurements
Augmenting local control networks with additional networked sensors and actuators poses a number of new challenges including the feedback of additional measurements that may be asynchronous and/or delayed like, for example, additional species concentrations or particle size distributions measurements. Furthermore, augmenting dedicated, local control networks (LCS) with additional networked sensor and actuator gives rise to the need to design/redesign and coordinate separate control systems that operate on the process. Model predictive control (MPC) is a natural control framework to deal with the design of coordinated, distributed control systems because of its ability to handle input and state constraints, and also because it can account for the actions of other actuators in computing the control action of a given set of control actuators in real-time. Motivated by the lack of available methods for the design of networked control systems (NCS) for chemical processes, in a recent work , we proposed a distributed model predictive control method for the design of networked control systems where both the pre-existing local control system and the networked control system are designed via Lyapunov-based model predictive control. This distributed MPC design utilizes continuous feedback, requires one-directional communication between the two distributed controllers, and may reduce the computational burden in the evaluation of the optimal manipulated inputs compared with a fully centralized LMPC of the same input/output-space dimension. Moreover, this distributed MPC design provides the potential of maintaining stability and performance in the face of new/failing actuators. In the present work, our objective is to extent our recent results  to develop distributed model predictive control algorithms for nonlinear systems subject to asynchronous and delayed measurements.
With respect to available results on distributed MPC design, several distributed MPC methods have been proposed in the literature that deal with the coordination of separate MPC controllers that communicate in order to obtain optimal input trajectories in a distributed manner. All of the above results on distributed MPC design are based on the assumption of continuous sampling and perfect communication between the sensor and the controller. Previous work on MPC design for systems subject to asynchronous or delayed measurements has primarily focused on centralized MPC design and has not addressed distributed model predictive control with the exception of a recent paper which addresses the issue of delays in the communication between the distributed controllers .
Motivated by the above considerations, this work focuses on distributed model predictive control of nonlinear systems subject to asynchronous and delayed measurements. In the case of asynchronous feedback, under the assumption that there exists an upper bound on the interval between two successive measurements of the system state, distributed Lyapunov-based model predictive controllers are designed that utilize one-directional communication and coordinate their actions to ensure that the state of the closed-loop system is ultimately bounded in a region that contains the origin. Subsequently, we focus on distributed model predictive control of nonlinear systems subject to asynchronous measurements that also involve time-delays. Under the assumption that there exists an upper bound on the maximum measurement delay, a distributed Lyapunov-based model predictive control design is proposed that utilizes two-directional communication between the distributed MPCs and takes the measurement delays explicitly into account to enforce practical stability in the closed-loop system. The applicability and effectiveness of the proposed control methods are illustrated through a chemical process example.
 J. Liu, D. Munoz de la Pena, and P. D. Christofides. Distributed model predictive control of nonlinear process systems, AIChE Journal, vol. 55, pp.1171-1184, 2009.
 E. Franco, L. Magni, T. Parisini, M. M. Polycarpou, and D. M. Raimondo. Cooperative constrained control of distributed agents with nonlinear dynamics and delayed information exchange: A stabilizing receding horizon approach. IEEE Transactions on Automatic Control, vol. 53, pp. 324-338, 2008.